Limits to Hole Mobility and Doping in Copper Iodide

Over one hundred years have passed since the discovery of the p-type transparent conducting material copper iodide, predating the concept of the “electron–hole” itself. Supercentenarian status notwithstanding, little is understood about the charge transport mechanisms in CuI. Herein, a variety of modeling techniques are used to investigate the charge transport properties of CuI, and limitations to the hole mobility over experimentally achievable carrier concentrations are discussed. Poor dielectric response is responsible for extensive scattering from ionized impurities at degenerately doped carrier concentrations, while phonon scattering is found to dominate at lower carrier concentrations. A phonon-limited hole mobility of 162 cm2 V–1 s–1 is predicted at room temperature. The simulated charge transport properties for CuI are compared to existing experimental data, and the implications for future device performance are discussed. In addition to charge transport calculations, the defect chemistry of CuI is investigated with hybrid functionals, revealing that reasonably localized holes from the copper vacancy are the predominant source of charge carriers. The chalcogens S and Se are investigated as extrinsic dopants, where it is found that despite relatively low defect formation energies, they are unlikely to act as efficient electron acceptors due to the strong localization of holes and subsequent deep transition levels.


Charge Transport
: IBTE hole mobility in CuI as a function of the kand q-point grids at 300K using different treatments (the density of q-points is the same as the density of k-points).Due to their long-range nature, quadrupolar interactions must be taken into account for an accurate description of the scattering potential and mobilities.Figure S3: CuI hole mobility against T computed with different methods.This graph shows the influence of dielectric constants on the results obtained with AMSET but also demonstrates the effect of the use of SERTA in the calculation of POP with AMSET whose results are close to the results obtained with this same approximation in ABINIT.

Defects
The ShakeNBreak method was used to identify the lowest energy structures for point defects in CuI. 3,4Upon generation of a defect, a series of targeted bond distortions (the quantity and direction of which are determined using simple valence chemistry rules) is applied, followed by a small, random "rattling" of the structure, in order to break the local symmetry.
These distorted structures, along with the "unperturbed" starting structure, are then relaxed using coarse calculation parameters to get a relatively cheap sampling of the complex defect potential energy surface.The lowest energy structure identified from this initial search is then relaxed using full accuracy parameters.This method allows the search for a defect ground state to begin from several, distinct points on the potential energy surface, decreasing the probability of getting stuck in a high energy local minimum.

Copper vacancy
Several metastable structures with energy less than 1 meV difference from the structure used to plot the transition level diagrams were identified using the ShakeNBreak method.Their relative energies are shown in Figure S5.The charge localisation is different between the structures, with Figure S6 showing the difference between the 'unperturbed" (no distortions) and lowest energy (−50% bond distortion) structures.The energy difference is so small that at finite temperature, it is likely that the real charge density is some combination of the two, indicating a reasonably delocalised charge density (as stated in the main text).

Iodine vacancy
The iodine vacancy was investigated in the charge states 1−, 0 and 1+, following reports from previous computational studies of a 1 + /1− transition level. 5The ground state of the neutral vacancy is found by a 20% bond distortion, shown in Figure S7a, and sees an opposite pair of Cu atoms relax into the vacancy, while another pair relax away from it.
The structure obtained from the "unperturbed" relaxation is significantly different, shown Cu atoms, and is 100 meV higher in energy.It is possible that this higher energy structure is the one identified by previous studies, pushing the neutral defect higher in energy on the transition level diagram and facilitating the negative-U behaviour.The fully ionised ground state iodine vacancy is shown in Figure S7c, and is a simple outward relaxation of the Cu atoms around the vacancy, caused by the removal of a centre of negative charge.
This example demonstrates the importance of sampling the potential energy surface thoroughly, although admittedly for the iodine vacancy the formation energies are so high that these differences in defect geometry play little to no rôle in the overall defect chemistry of CuI.4.17 0 0 0 4.17 0 0 0 4.17 N k × N k × N k k-with SOC & mobilities with SOC and Q* Phonons with SOC & mobilities with SOC and without Q* Phonons without SOC & mobilities with SOC and Q* Phonons without SOC & mobilities without SOC and with Q* Low carrier concentration, 1 × 10 16 cm −3 .High carrier concentration, 1×10 20 cm −3 .

Figure S4 :
Figure S4: CuI hole mobility as a function of temperature at two carrier concentrations showing the dominant scattering mechanism and the dependence on the value of ϵ 0 .

Figure S5 :
Figure S5: Energy profile of relaxed copper vacancies with various bond distortions.

Figure S6 :
Figure S6: Geometries and partial charge density of the copper vacancy.

Figure S8 :
Figure S8: Convergence of the low-frequency dielectric response against plane-wave energy cut-off for the copper halides.